I will describe the votlage, megawatts, megavars (receieved and delivered), and power factor (lagging and leading) in terms of the electricity. Key goals are to understand substations and meters with regards to voltage and power factor as well as megawatts and megavars and to review the relatioship between power factor and voltage.
Electric utilities collect meter readings in time intervals in various units. The intervals can be from 1 minute to 60 minute intervals collecing kW, kWh, VARh, volts. An utility needs to maintain a specified range for voltage across their electric network. When voltage is too low brown outs or electric motors may fail to work and when voltage is too high appliances and equiment can overheat, burn up, and possibly explode.
“A negative power factor (Lagging) occurs when the device (which is normally the load) generates power, which then flows back towards the source, which is normally considered the generator.”[1]
“In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.” [1]
“Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts).
This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled.” [1] (since they are proportional to the square of the current).
“Alternatively all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current.” [1]
“Utilities typically charge additional costs to commercial customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.” [1]
Power factors are usually stated as “leading” or “lagging” to show the sign of the phase angle. Capacitive loads are leading (current leads voltage) and supply power, and inductive loads are lagging (current lags voltage) and consume power.
Range of days: 2016-02-28, 2016-03-09
Summary of Voltage: 100.6, 120.8, 122.4, 122, 123.4, 130
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 100.6 120.8 122.4 122.0 123.4 130.0
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 5.832 7.704 8.962 10.840 25.240
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -3.572 -1.274 -0.754 -0.237 0.752 7.080 240
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.000 0.567 1.210 3.040 2.760 50.130 240
The voltage dataset contains endpoints collecting readings every 15 minutes.
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 3031348 obs. of 10 variables:
## $ substationName: chr "HIGHLAND PARK" "DALLAS" "HIGHLAND PARK" "HOUSTON" ...
## $ meter : Factor w/ 2939 levels "200001","200002",..: 637 1979 38 1419 2335 2437 1806 346 2794 615 ...
## $ readdate : Factor w/ 1056 levels "2016-02-28 00:15:00",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ dtReadDate : POSIXct, format: "2016-02-28" "2016-02-28" ...
## $ dtReadDay : POSIXct, format: "2016-02-28" "2016-02-28" ...
## $ h : num 0 0 0 0 0 0 0 0 0 0 ...
## $ hm : chr "00:15" "00:15" "00:15" "00:15" ...
## $ Voltage : num 226 230 230 230 230 ...
## $ VoltsHalf : num 113 115 115 115 115 ...
## $ voltage.bucket: Factor w/ 4 levels "(0,114]","(114,120]",..: 1 2 2 2 2 2 2 2 2 2 ...
The power factor dataset contains endpoints collecting readings every 60 minutes.
## Classes 'tbl_df', 'tbl' and 'data.frame': 3600 obs. of 16 variables:
## $ substationName: chr "ARLINGTON" "ARLINGTON" "ARLINGTON" "ARLINGTON" ...
## $ ReadDate : Factor w/ 240 levels "2016-02-28 00:10:00.000",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ dtReadDate : POSIXct, format: "2016-02-28 00:10:00" "2016-02-28 01:10:00" ...
## $ dtReadDay : POSIXct, format: "2016-02-28" "2016-02-28" ...
## $ h : num 0 1 2 3 4 5 6 7 8 9 ...
## $ mw : num 8.8 8.75 8.92 9.17 9.55 ...
## $ mvar.delivered: num 0.913 0.92 0.946 1.004 1.067 ...
## $ mvar.received : num 0 0 0 0 0 ...
## $ mvar : num 0.913 0.92 0.946 1.004 1.067 ...
## $ mwsquared : num 77.5 76.5 79.5 84.1 91.3 ...
## $ mvarsquared : num 0.834 0.846 0.895 1.008 1.138 ...
## $ va : num 8.85 8.79 8.97 9.22 9.61 ...
## $ pf : num 0.995 0.995 0.994 0.994 0.994 ...
## $ pfChart : num 0.995 0.995 0.994 0.994 0.994 ...
## $ desc : Factor w/ 2 levels "Lagging","Leading": 1 1 1 1 1 1 2 2 2 2 ...
## $ pf.range : Factor w/ 7 levels "(0,0.88.]","(0.88,0.90]",..: 7 7 7 7 7 7 7 6 6 6 ...
Used for mapping the Voltage and Power Factor datasets together.
## 'data.frame': 27 obs. of 2 variables:
## $ station : Factor w/ 27 levels "BOYN","CHPH",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ substationName: Factor w/ 27 levels "Arlington","Austin",..: 4 9 5 17 11 24 6 26 10 15 ...
## 'data.frame': 3033369 obs. of 4 variables:
## $ readdate : Factor w/ 1056 levels "2016-02-28 00:15:00",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ Voltage : num 235 237 237 236 236 ...
## $ substationName: Factor w/ 24 levels "Area 51","Arlington",..: 12 12 12 12 12 12 12 12 12 12 ...
## $ meter : int 300063 300063 300063 300063 300063 300063 300063 300063 300063 300063 ...
## 'data.frame': 10800 obs. of 4 variables:
## $ ReadValue: num 0 0 0 0 0 0 0 0 0 0 ...
## $ station : Factor w/ 15 levels "BOYN","CHPH",..: 4 4 4 4 4 4 4 4 4 4 ...
## $ name : Factor w/ 3 levels "PMQD3D","PMQD3R",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ ReadDate : Factor w/ 240 levels "2016-02-28 00:10:00.000",..: 1 2 3 4 5 6 235 236 237 238 ...
Voltage and Power Factor by time interval for each deliver point (substation) are the main features. One goal is to determine if we can predict power factor.
investigation into your feature(s) of interest? * mega watt
* mega var delivered
* mega var received
I created the power factor, mvars and the direction of the power factor (lagging and leading).
New variables where created for these datasets:
Austin and Dallas have bimodel distibutions of voltage for the days being reviewed.
The long leading tail on the voltage histogram, has a larger range in the data in the lower range than in the upper range.
Number of voltage intervals < 117: 43458
The range is : 100.6, 116.95
Number of voltage intervals > 126: 41439
The range is : 126.05, 129.95
Various methods were used to clean the data. For instance the ReadDates for the voltage intervals are in ending interval. The interval starts at 3/2/2016 00:15min and ends on 3/3/2016 00:00. To associate the 15 minute intervals with the correct hour and day, we had to roll back each 15 minute interval by 15 minutes.
The power factor data needed to be pivoted to get the data into a tidy format as well. The orignal data has the MegaWatt, MegaVars Delivered and Received in the same column, these values were split out into their own columns.
The substation names can have leading and trailing spaces so this data needed to be trimed.
The scatter plot shows the data along the time axis for the intervals for the day. The interesting point in this chart, which is similar to the histogram is how the shading changes from dark to grey, which is the points stacking on top of each other.
It takes 5 points on top of each other to make a solid point on this chart.
This demonstrates how the data is spread out over the ranges through the day by hour.
We can see there seems to be one metering point with high voltage which is consistently above the other voltage readings.
## [1] 0.8827947
If we search all the meters on the Dallas substation, and sort descending by voltage we can obtain a list of meters with the highest voltage.
| meter | dtReadDay | v.min | v.mean | v.median | v.max | v.intervals |
|---|---|---|---|---|---|---|
| 300686 | 2016-03-06 | 126.15 | 127.5969 | 127.450 | 129.15 | 96 |
| 300686 | 2016-02-29 | 116.65 | 124.7021 | 124.675 | 129.00 | 96 |
| 300686 | 2016-03-09 | 112.65 | 120.2797 | 118.900 | 128.90 | 96 |
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 100.6 120.8 122.4 122.0 123.4 130.0
## [1] 2.047819
## [1] 100.60 129.95
## 0% 25% 50% 75% 100%
## 100.60 120.80 122.35 123.45 129.95
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 5.832 7.704 8.962 10.840 25.240
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -3.572 -1.274 -0.754 -0.237 0.752 7.080 240
The multiple points are the 11 days we have in this dataset.
Meters where more than 4 intervals below the 114 volts threshold.
| substationName | meter | dtReadDay | count |
|---|---|---|---|
| HIGHLAND PARK | 301146 | 2016-03-03 | 35 |
| DALLAS | 200227 | 2016-03-03 | 31 |
| HIGHLAND PARK | 301146 | 2016-02-28 | 28 |
| AUSTIN | 300964 | 2016-03-03 | 27 |
| HIGHLAND PARK | 300482 | 2016-03-03 | 27 |
| HIGHLAND PARK | 301146 | 2016-03-01 | 23 |
| HIGHLAND PARK | 301146 | 2016-03-07 | 23 |
| HIGHLAND PARK | 300482 | 2016-03-01 | 21 |
| IRVING | 301042 | 2016-03-05 | 21 |
| CARROLTON | 200811 | 2016-03-06 | 20 |
Meters where more than 4 intervals below the 126 volts threshold.
| substationName | meter | dtReadDay | count |
|---|---|---|---|
| ARLINGTON | 200277 | 2016-03-02 | 1 |
| ARLINGTON | 201979 | 2016-03-03 | 1 |
| ARLINGTON | 201979 | 2016-03-02 | 6 |
| ARLINGTON | 300872 | 2016-03-03 | 3 |
| ARLINGTON | 300872 | 2016-03-05 | 4 |
| ARLINGTON | 300872 | 2016-03-02 | 9 |
| ARLINGTON | 301334 | 2016-03-05 | 1 |
| ARLINGTON | 301334 | 2016-02-28 | 2 |
| ARLINGTON | 301796 | 2016-02-28 | 1 |
| ARLINGTON | 301796 | 2016-03-05 | 2 |
By Hour
By Hour
This shows an interesting trend starting at 11AM (11:00 hours) until 10PM (20:00 hrs). The power factor spreads over a wider range. This is interesting on a system wide review, however we are more concerned with the power factor for each delivery point.
The strongest relationship I found is between megawatts and power factor.
As the megawatts increases the power factor approaches the 1, for each of the Substations for this single day investigation.
Coefficient, r
| Strength of Association | Positive | Negative |
|---|---|---|
| Small | .1 to .3 | -0.1 to -0.3 |
| Medium | .3 to .5 | -0.3 to -0.5 |
| Large | .5 to 1.0 | -0.5 to -1.0 |
Review the correlation between power factor and voltage using Pearsons.
Review the correlation between power factor and voltage using Pearsons.
##
## Pearson's product-moment correlation
##
## data: summary_total$v.mean and summary_total$pf
## t = -3.7994, df = 3104, p-value = 0.0001478
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.10296188 -0.03294618
## sample estimates:
## cor
## -0.0680378
Counts of the voltage instances in each bucketed range.
## (0,114] (114,120] (120,126] (126,140]
## 1958 520655 2467296 41439
| dtReadDay | substationName | (0,114] | (114,120] | (120,126] | (126,140] | total | p1 | p2 | p3 | p4 |
|---|---|---|---|---|---|---|---|---|---|---|
| 2016-02-28 | AREA 51 | NA | 164 | 4634 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | ARLINGTON | 1 | 738 | 9526 | 3 | 10268 | 0.0097390 | 7.1873783 | 92.77367 | 0.0292170 |
| 2016-02-28 | AUSTIN | 16 | 9227 | 4289 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | CARROLTON | NA | 967 | 7864 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | DALLAS | 35 | 12337 | 6815 | 6 | 19193 | 0.1823582 | 64.2786433 | 35.50774 | 0.0312614 |
| 2016-02-28 | EULESS | NA | 160 | 7230 | 1 | NA | NA | NA | NA | NA |
| 2016-02-28 | FORNEY | NA | 212 | 8131 | 111 | NA | NA | NA | NA | NA |
| 2016-02-28 | FT WORTH | NA | 934 | 14332 | 92 | NA | NA | NA | NA | NA |
| 2016-02-28 | GARLAND | NA | 504 | 16940 | 24 | NA | NA | NA | NA | NA |
| 2016-02-28 | HIGHLAND PARK | 143 | 15510 | 9972 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | HILLSBORO | NA | 48 | 8014 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | HOUSTON | 33 | 11579 | 6144 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | IRVING | 7 | 3833 | 35505 | 5 | 39350 | 0.0177891 | 9.7407878 | 90.22872 | 0.0127065 |
| 2016-02-28 | MESQUITE | 7 | 1026 | 9332 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | MILFORD | NA | 74 | 2609 | 3 | NA | NA | NA | NA | NA |
| 2016-02-28 | MINERAL WELLS | NA | 175 | 2068 | 60 | NA | NA | NA | NA | NA |
| 2016-02-28 | RICHARDSON | NA | 1599 | 14423 | 10 | NA | NA | NA | NA | NA |
| 2016-02-28 | ROCKWALL | NA | 147 | 1067 | 226 | NA | NA | NA | NA | NA |
| 2016-02-28 | ROWLET | 2 | 800 | 18576 | 584 | 19962 | 0.0100190 | 4.0076145 | 93.05681 | 2.9255586 |
| 2016-02-28 | TEMPLE | 2 | 686 | 1808 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | UPTOWN | NA | 2 | 1564 | 2562 | NA | NA | NA | NA | NA |
| 2016-02-28 | VICTORIA | 1 | 225 | 2736 | 590 | 3552 | 0.0281532 | 6.3344595 | 77.02703 | 16.6103604 |
| 2016-02-28 | WACO | NA | 957 | 6816 | NA | NA | NA | NA | NA | NA |
| 2016-02-28 | WAXAHACHIE | NA | 68 | 3675 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | AREA 51 | NA | 56 | 4741 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | ARLINGTON | NA | 265 | 10003 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | AUSTIN | NA | 487 | 12948 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | CARROLTON | NA | 382 | 8449 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | DALLAS | 3 | 939 | 18382 | 160 | 19484 | 0.0153972 | 4.8193389 | 94.34408 | 0.8211866 |
| 2016-02-29 | EULESS | NA | 81 | 7307 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | FORNEY | NA | 75 | 8370 | 98 | NA | NA | NA | NA | NA |
| 2016-02-29 | FT WORTH | NA | 482 | 15055 | 72 | NA | NA | NA | NA | NA |
| 2016-02-29 | GARLAND | 11 | 324 | 17231 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | HIGHLAND PARK | 1 | 1092 | 24683 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | HILLSBORO | NA | 11 | 8051 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | HOUSTON | NA | 623 | 17127 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | IRVING | 3 | 2447 | 37055 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | MESQUITE | 7 | 504 | 9853 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | MILFORD | NA | 102 | 2586 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | MINERAL WELLS | NA | 31 | 2221 | 51 | NA | NA | NA | NA | NA |
| 2016-02-29 | RICHARDSON | 2 | 846 | 15180 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | ROCKWALL | NA | 66 | 1175 | 236 | NA | NA | NA | NA | NA |
| 2016-02-29 | ROWLET | 1 | 355 | 19641 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | TEMPLE | NA | 481 | 2014 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | UPTOWN | NA | 1 | 1224 | 2993 | NA | NA | NA | NA | NA |
| 2016-02-29 | VICTORIA | NA | 107 | 2772 | 673 | NA | NA | NA | NA | NA |
| 2016-02-29 | WACO | NA | 714 | 6964 | NA | NA | NA | NA | NA | NA |
| 2016-02-29 | WAXAHACHIE | NA | 87 | 3656 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | AREA 51 | NA | 93 | 4698 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | ARLINGTON | 8 | 675 | 9646 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | AUSTIN | 19 | 9973 | 3541 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | CARROLTON | NA | 943 | 7887 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | DALLAS | 56 | 14637 | 4764 | 6 | 19463 | 0.2877254 | 75.2042337 | 24.47721 | 0.0308277 |
| 2016-03-01 | EULESS | NA | 117 | 7464 | 3 | NA | NA | NA | NA | NA |
| 2016-03-01 | FORNEY | NA | 139 | 8360 | 32 | NA | NA | NA | NA | NA |
| 2016-03-01 | FT WORTH | 2 | 753 | 14799 | 79 | 15633 | 0.0127934 | 4.8167338 | 94.66513 | 0.5053413 |
| 2016-03-01 | GARLAND | NA | 477 | 17087 | 1 | NA | NA | NA | NA | NA |
| 2016-03-01 | HIGHLAND PARK | 164 | 20193 | 5456 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | HILLSBORO | NA | 45 | 8016 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | HOUSTON | 33 | 13977 | 3838 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | IRVING | 5 | 4657 | 34956 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | MESQUITE | 10 | 991 | 9439 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | MILFORD | NA | 121 | 2567 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | MINERAL WELLS | NA | 192 | 2102 | 8 | NA | NA | NA | NA | NA |
| 2016-03-01 | RICHARDSON | 5 | 1849 | 14176 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | ROCKWALL | NA | 121 | 1294 | 120 | NA | NA | NA | NA | NA |
| 2016-03-01 | ROWLET | 1 | 1191 | 19150 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | TEMPLE | NA | 539 | 1861 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | UPTOWN | NA | 4 | 1813 | 2500 | NA | NA | NA | NA | NA |
| 2016-03-01 | VICTORIA | 2 | 335 | 2840 | 375 | 3552 | 0.0563063 | 9.4313063 | 79.95495 | 10.5574324 |
| 2016-03-01 | WACO | NA | 1061 | 6705 | NA | NA | NA | NA | NA | NA |
| 2016-03-01 | WAXAHACHIE | NA | 102 | 3642 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | AREA 51 | NA | 368 | 4428 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | ARLINGTON | 3 | 947 | 9489 | 16 | 10455 | 0.0286944 | 9.0578670 | 90.76040 | 0.1530368 |
| 2016-03-02 | AUSTIN | 5 | 1888 | 11640 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | CARROLTON | 3 | 1991 | 7111 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | DALLAS | 6 | 2088 | 17228 | 141 | 19463 | 0.0308277 | 10.7280481 | 88.51667 | 0.7244515 |
| 2016-03-02 | EULESS | NA | 202 | 7365 | 17 | NA | NA | NA | NA | NA |
| 2016-03-02 | FORNEY | NA | 366 | 8198 | 71 | NA | NA | NA | NA | NA |
| 2016-03-02 | FT WORTH | 10 | 1383 | 15258 | 82 | 16733 | 0.0597621 | 8.2651049 | 91.18508 | 0.4900496 |
| 2016-03-02 | GARLAND | 2 | 698 | 16866 | 35 | 17601 | 0.0113630 | 3.9656838 | 95.82410 | 0.1988523 |
| 2016-03-02 | HIGHLAND PARK | 13 | 2618 | 23283 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | HILLSBORO | NA | 110 | 7953 | 1 | NA | NA | NA | NA | NA |
| 2016-03-02 | HOUSTON | 3 | 2283 | 15654 | 6 | 17946 | 0.0167168 | 12.7214978 | 87.22835 | 0.0334336 |
| 2016-03-02 | IRVING | 16 | 6261 | 33723 | 56 | 40056 | 0.0399441 | 15.6306171 | 84.18963 | 0.1398043 |
| 2016-03-02 | MESQUITE | 27 | 1987 | 8449 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | MILFORD | 1 | 271 | 2510 | 2 | 2784 | 0.0359195 | 9.7341954 | 90.15805 | 0.0718391 |
| 2016-03-02 | MINERAL WELLS | NA | 400 | 1903 | 1 | NA | NA | NA | NA | NA |
| 2016-03-02 | RICHARDSON | 16 | 3274 | 12834 | 1 | 16125 | 0.0992248 | 20.3038760 | 79.59070 | 0.0062016 |
| 2016-03-02 | ROCKWALL | NA | 294 | 1199 | 43 | NA | NA | NA | NA | NA |
| 2016-03-02 | ROWLET | 34 | 4805 | 15508 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | TEMPLE | 3 | 938 | 1458 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | UPTOWN | NA | 18 | 2889 | 1412 | NA | NA | NA | NA | NA |
| 2016-03-02 | VICTORIA | 4 | 722 | 2618 | 304 | 3648 | 0.1096491 | 19.7916667 | 71.76535 | 8.3333333 |
| 2016-03-02 | WACO | 6 | 2120 | 5689 | NA | NA | NA | NA | NA | NA |
| 2016-03-02 | WAXAHACHIE | NA | 149 | 3594 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | AREA 51 | NA | 273 | 4620 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | ARLINGTON | NA | 739 | 9716 | 4 | NA | NA | NA | NA | NA |
| 2016-03-03 | AUSTIN | 49 | 8224 | 5260 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | CARROLTON | 1 | 1797 | 7319 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | DALLAS | 81 | 12596 | 6512 | 5 | 19194 | 0.4220069 | 65.6246744 | 33.92727 | 0.0260498 |
| 2016-03-03 | EULESS | NA | 83 | 7485 | 16 | NA | NA | NA | NA | NA |
| 2016-03-03 | FORNEY | NA | 353 | 8251 | 33 | NA | NA | NA | NA | NA |
| 2016-03-03 | FT WORTH | 2 | 1294 | 15591 | 94 | 16981 | 0.0117779 | 7.6202815 | 91.81438 | 0.5535599 |
| 2016-03-03 | GARLAND | NA | 574 | 17003 | 119 | NA | NA | NA | NA | NA |
| 2016-03-03 | HIGHLAND PARK | 181 | 16480 | 9251 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | HILLSBORO | NA | 50 | 8011 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | HOUSTON | 39 | 10545 | 7268 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | IRVING | 11 | 5830 | 34367 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | MESQUITE | 21 | 1864 | 8578 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | MILFORD | NA | 272 | 2410 | 4 | NA | NA | NA | NA | NA |
| 2016-03-03 | MINERAL WELLS | NA | 396 | 1908 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | RICHARDSON | 8 | 2804 | 13408 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | ROCKWALL | NA | 273 | 1256 | 7 | NA | NA | NA | NA | NA |
| 2016-03-03 | ROWLET | 23 | 4193 | 16128 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | TEMPLE | 3 | 1411 | 1082 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | UPTOWN | NA | 3 | 2716 | 1598 | NA | NA | NA | NA | NA |
| 2016-03-03 | VICTORIA | NA | 460 | 3167 | 21 | NA | NA | NA | NA | NA |
| 2016-03-03 | WACO | 1 | 1480 | 6292 | NA | NA | NA | NA | NA | NA |
| 2016-03-03 | WAXAHACHIE | NA | 117 | 3627 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | AREA 51 | NA | 343 | 4550 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | ARLINGTON | 3 | 933 | 9525 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | AUSTIN | 1 | 1126 | 12308 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | CARROLTON | NA | 1453 | 7664 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | DALLAS | 11 | 1735 | 17450 | 95 | 19291 | 0.0570214 | 8.9938313 | 90.45669 | 0.4924576 |
| 2016-03-04 | EULESS | NA | 212 | 7368 | 3 | NA | NA | NA | NA | NA |
| 2016-03-04 | FORNEY | NA | 328 | 8121 | 88 | NA | NA | NA | NA | NA |
| 2016-03-04 | FT WORTH | 2 | 1484 | 15516 | 79 | 17081 | 0.0117089 | 8.6880159 | 90.83777 | 0.4625022 |
| 2016-03-04 | GARLAND | 3 | 744 | 16758 | 17 | 17522 | 0.0171213 | 4.2460906 | 95.63977 | 0.0970209 |
| 2016-03-04 | HIGHLAND PARK | 1 | 2656 | 23285 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | HILLSBORO | NA | 39 | 8022 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | HOUSTON | NA | 1624 | 16229 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | IRVING | 10 | 6349 | 34140 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | MESQUITE | 13 | 1774 | 8578 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | MILFORD | NA | 240 | 2443 | 4 | NA | NA | NA | NA | NA |
| 2016-03-04 | MINERAL WELLS | NA | 319 | 1807 | 82 | NA | NA | NA | NA | NA |
| 2016-03-04 | RICHARDSON | 7 | 2602 | 13324 | 1 | 15934 | 0.0439312 | 16.3298607 | 83.61993 | 0.0062759 |
| 2016-03-04 | ROCKWALL | NA | 205 | 1245 | 85 | NA | NA | NA | NA | NA |
| 2016-03-04 | ROWLET | 9 | 2889 | 17361 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | TEMPLE | NA | 1069 | 1426 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | UPTOWN | NA | 4 | 2225 | 2089 | NA | NA | NA | NA | NA |
| 2016-03-04 | VICTORIA | NA | 413 | 2694 | 445 | NA | NA | NA | NA | NA |
| 2016-03-04 | WACO | 3 | 1583 | 6148 | NA | NA | NA | NA | NA | NA |
| 2016-03-04 | WAXAHACHIE | NA | 95 | 3648 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | AREA 51 | NA | 299 | 4595 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | ARLINGTON | 3 | 818 | 9632 | 7 | 10460 | 0.0286807 | 7.8202677 | 92.08413 | 0.0669216 |
| 2016-03-05 | AUSTIN | 47 | 8564 | 4824 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | CARROLTON | 14 | 1577 | 7529 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | DALLAS | 54 | 13628 | 5797 | 5 | 19484 | 0.2771505 | 69.9445699 | 29.75262 | 0.0256621 |
| 2016-03-05 | EULESS | NA | 174 | 7408 | 1 | NA | NA | NA | NA | NA |
| 2016-03-05 | FORNEY | NA | 260 | 8107 | 170 | NA | NA | NA | NA | NA |
| 2016-03-05 | FT WORTH | NA | 1054 | 15922 | 88 | NA | NA | NA | NA | NA |
| 2016-03-05 | GARLAND | NA | 661 | 16739 | 68 | NA | NA | NA | NA | NA |
| 2016-03-05 | HIGHLAND PARK | 88 | 15378 | 10541 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | HILLSBORO | NA | 77 | 7985 | 1 | NA | NA | NA | NA | NA |
| 2016-03-05 | HOUSTON | 18 | 10935 | 6611 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | IRVING | 26 | 5275 | 35169 | 31 | 40501 | 0.0641959 | 13.0243698 | 86.83489 | 0.0765413 |
| 2016-03-05 | MESQUITE | 30 | 1470 | 8865 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | MILFORD | NA | 188 | 2493 | 6 | NA | NA | NA | NA | NA |
| 2016-03-05 | MINERAL WELLS | NA | 268 | 1912 | 28 | NA | NA | NA | NA | NA |
| 2016-03-05 | RICHARDSON | 6 | 2403 | 13519 | 5 | 15933 | 0.0376577 | 15.0819055 | 84.84906 | 0.0313814 |
| 2016-03-05 | ROCKWALL | 2 | 201 | 1191 | 141 | 1535 | 0.1302932 | 13.0944625 | 77.58958 | 9.1856678 |
| 2016-03-05 | ROWLET | 15 | 1733 | 18489 | 108 | 20345 | 0.0737282 | 8.5180634 | 90.87737 | 0.5308430 |
| 2016-03-05 | TEMPLE | 1 | 637 | 1761 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | UPTOWN | NA | 31 | 1685 | 2603 | NA | NA | NA | NA | NA |
| 2016-03-05 | VICTORIA | NA | 438 | 2581 | 533 | NA | NA | NA | NA | NA |
| 2016-03-05 | WACO | NA | 1377 | 6490 | NA | NA | NA | NA | NA | NA |
| 2016-03-05 | WAXAHACHIE | NA | 83 | 3660 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | AREA 51 | NA | 144 | 4749 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | ARLINGTON | 1 | 848 | 9611 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | AUSTIN | 9 | 1100 | 12422 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | CARROLTON | 24 | 1268 | 7827 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | DALLAS | 2 | 1461 | 17881 | 238 | 19582 | 0.0102135 | 7.4609335 | 91.31345 | 1.2154019 |
| 2016-03-06 | EULESS | NA | 219 | 7365 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | FORNEY | NA | 267 | 8415 | 53 | NA | NA | NA | NA | NA |
| 2016-03-06 | FT WORTH | NA | 1192 | 15819 | 74 | NA | NA | NA | NA | NA |
| 2016-03-06 | GARLAND | NA | 665 | 17176 | 11 | NA | NA | NA | NA | NA |
| 2016-03-06 | HIGHLAND PARK | 3 | 2310 | 23692 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | HILLSBORO | NA | 51 | 8108 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | HOUSTON | 1 | 1282 | 16278 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | IRVING | 16 | 4775 | 36190 | 2 | 40983 | 0.0390406 | 11.6511724 | 88.30491 | 0.0048801 |
| 2016-03-06 | MESQUITE | 22 | 1465 | 8975 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | MILFORD | NA | 199 | 2489 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | MINERAL WELLS | NA | 208 | 2094 | 1 | NA | NA | NA | NA | NA |
| 2016-03-06 | RICHARDSON | 6 | 2160 | 14047 | 5 | 16218 | 0.0369959 | 13.3185350 | 86.61364 | 0.0308299 |
| 2016-03-06 | ROCKWALL | NA | 162 | 1233 | 141 | NA | NA | NA | NA | NA |
| 2016-03-06 | ROWLET | 6 | 1329 | 19104 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | TEMPLE | 1 | 636 | 1763 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | UPTOWN | NA | 1 | 1586 | 2729 | NA | NA | NA | NA | NA |
| 2016-03-06 | VICTORIA | NA | 382 | 3003 | 167 | NA | NA | NA | NA | NA |
| 2016-03-06 | WACO | NA | 1359 | 6607 | NA | NA | NA | NA | NA | NA |
| 2016-03-06 | WAXAHACHIE | NA | 59 | 3684 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | AREA 51 | NA | 89 | 4807 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | ARLINGTON | NA | 430 | 10128 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | AUSTIN | 21 | 11206 | 2308 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | CARROLTON | 2 | 774 | 8343 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | DALLAS | 34 | 14498 | 4852 | 5 | 19389 | 0.1753572 | 74.7743566 | 25.02450 | 0.0257878 |
| 2016-03-07 | EULESS | NA | 63 | 7615 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | FORNEY | NA | 147 | 8512 | 77 | NA | NA | NA | NA | NA |
| 2016-03-07 | FT WORTH | NA | 538 | 16630 | 81 | NA | NA | NA | NA | NA |
| 2016-03-07 | GARLAND | 6 | 362 | 17579 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | HIGHLAND PARK | 99 | 19063 | 6846 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | HILLSBORO | NA | 14 | 8145 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | HOUSTON | 19 | 15394 | 2438 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | IRVING | 13 | 4272 | 36735 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | MESQUITE | 7 | 792 | 9757 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | MILFORD | NA | 168 | 2519 | 1 | NA | NA | NA | NA | NA |
| 2016-03-07 | MINERAL WELLS | NA | 87 | 2021 | 195 | NA | NA | NA | NA | NA |
| 2016-03-07 | RICHARDSON | 1 | 1061 | 15159 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | ROCKWALL | NA | 73 | 1210 | 253 | NA | NA | NA | NA | NA |
| 2016-03-07 | ROWLET | 1 | 546 | 19898 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | TEMPLE | NA | 552 | 1944 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | UPTOWN | NA | 4 | 1203 | 3112 | NA | NA | NA | NA | NA |
| 2016-03-07 | VICTORIA | NA | 200 | 2426 | 926 | NA | NA | NA | NA | NA |
| 2016-03-07 | WACO | NA | 725 | 7241 | NA | NA | NA | NA | NA | NA |
| 2016-03-07 | WAXAHACHIE | NA | 62 | 3682 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | AREA 51 | NA | 30 | 4865 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | ARLINGTON | NA | 195 | 10359 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | AUSTIN | NA | 586 | 12948 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | CARROLTON | 3 | 380 | 9023 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | DALLAS | 2 | 1104 | 18310 | 69 | 19485 | 0.0102643 | 5.6658968 | 93.96972 | 0.3541186 |
| 2016-03-08 | EULESS | NA | 75 | 7604 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | FORNEY | NA | 62 | 8753 | 135 | NA | NA | NA | NA | NA |
| 2016-03-08 | FT WORTH | 16 | 556 | 17285 | 87 | 17944 | 0.0891663 | 3.0985288 | 96.32746 | 0.4848417 |
| 2016-03-08 | GARLAND | 6 | 247 | 17722 | 3 | 17978 | 0.0333741 | 1.3739014 | 98.57604 | 0.0166871 |
| 2016-03-08 | HIGHLAND PARK | 1 | 846 | 25257 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | HILLSBORO | 1 | 20 | 8138 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | HOUSTON | NA | 571 | 17090 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | IRVING | 3 | 2656 | 38606 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | MESQUITE | 6 | 420 | 10129 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | MILFORD | 1 | 115 | 2666 | 2 | 2784 | 0.0359195 | 4.1307471 | 95.76149 | 0.0718391 |
| 2016-03-08 | MINERAL WELLS | NA | 35 | 2140 | 174 | NA | NA | NA | NA | NA |
| 2016-03-08 | RICHARDSON | 1 | 751 | 15467 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | ROCKWALL | NA | 64 | 1111 | 361 | NA | NA | NA | NA | NA |
| 2016-03-08 | ROWLET | NA | 270 | 20171 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | TEMPLE | NA | 384 | 2112 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | UPTOWN | NA | NA | 570 | 3747 | NA | NA | NA | NA | NA |
| 2016-03-08 | VICTORIA | NA | 76 | 2584 | 890 | NA | NA | NA | NA | NA |
| 2016-03-08 | WACO | NA | 353 | 7612 | NA | NA | NA | NA | NA | NA |
| 2016-03-08 | WAXAHACHIE | NA | 65 | 3678 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | AREA 51 | NA | 43 | 4882 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | ARLINGTON | NA | 134 | 10421 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | AUSTIN | 18 | 10184 | 3331 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | CARROLTON | 2 | 267 | 9383 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | DALLAS | 17 | 13134 | 6297 | 27 | 19475 | 0.0872914 | 67.4403081 | 32.33376 | 0.1386393 |
| 2016-03-09 | EULESS | NA | 86 | 7594 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | FORNEY | NA | 34 | 8899 | 221 | NA | NA | NA | NA | NA |
| 2016-03-09 | FT WORTH | 1 | 474 | 17823 | 82 | 18380 | 0.0054407 | 2.5788901 | 96.96953 | 0.4461371 |
| 2016-03-09 | GARLAND | 13 | 77 | 17945 | 5 | 18040 | 0.0720621 | 0.4268293 | 99.47339 | 0.0277162 |
| 2016-03-09 | HIGHLAND PARK | 35 | 22963 | 3201 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | HILLSBORO | NA | 10 | 8148 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | HOUSTON | 9 | 13316 | 4330 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | IRVING | 4 | 2065 | 39286 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | MESQUITE | 3 | 220 | 10237 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | MILFORD | NA | 125 | 2772 | 3 | NA | NA | NA | NA | NA |
| 2016-03-09 | MINERAL WELLS | NA | 15 | 2211 | 172 | NA | NA | NA | NA | NA |
| 2016-03-09 | RICHARDSON | 3 | 417 | 15803 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | ROCKWALL | NA | 53 | 1134 | 348 | NA | NA | NA | NA | NA |
| 2016-03-09 | ROWLET | NA | 263 | 20083 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | TEMPLE | NA | 235 | 2165 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | UPTOWN | NA | NA | 437 | 3879 | NA | NA | NA | NA | NA |
| 2016-03-09 | VICTORIA | NA | 77 | 2896 | 607 | NA | NA | NA | NA | NA |
| 2016-03-09 | WACO | NA | 105 | 7766 | NA | NA | NA | NA | NA | NA |
| 2016-03-09 | WAXAHACHIE | NA | 80 | 3664 | NA | NA | NA | NA | NA | NA |
Counts of the voltage instances in each bucketed range by hour by substations
## (0,114] (114,120] (120,126] (126,140]
## 1958 520655 2467296 41439
Create a line graph of voltages vs. h so that each voltage.bucket is a line tracking the median user voltage counts across hour.
## substationName ReadDate
## Length:240 2016-02-28 00:10:00.000: 1
## Class :character 2016-02-28 01:10:00.000: 1
## Mode :character 2016-02-28 02:10:00.000: 1
## 2016-02-28 03:10:00.000: 1
## 2016-02-28 04:10:00.000: 1
## 2016-02-28 05:10:00.000: 1
## (Other) :234
## dtReadDate dtReadDay
## Min. :2016-02-28 00:10:00 Min. :2016-02-28 00:00:00
## 1st Qu.:2016-03-01 11:55:00 1st Qu.:2016-03-01 00:00:00
## Median :2016-03-03 23:40:00 Median :2016-03-03 12:00:00
## Mean :2016-03-03 23:40:00 Mean :2016-03-03 12:00:00
## 3rd Qu.:2016-03-06 11:25:00 3rd Qu.:2016-03-06 00:00:00
## Max. :2016-03-08 23:10:00 Max. :2016-03-08 00:00:00
##
## h mw mvar.delivered mvar.received
## Min. : 0.00 Min. : 0.000 Min. :0.00000 Min. :0.000
## 1st Qu.: 5.75 1st Qu.: 6.369 1st Qu.:0.00000 1st Qu.:1.059
## Median :11.50 Median : 8.251 Median :0.00000 Median :1.492
## Mean :11.50 Mean : 8.514 Mean :0.01423 Mean :1.526
## 3rd Qu.:17.25 3rd Qu.:10.579 3rd Qu.:0.00000 3rd Qu.:2.084
## Max. :23.00 Max. :14.602 Max. :0.69300 Max. :2.416
##
## mvar mwsquared mvarsquared va
## Min. :-2.416 Min. : 0.00 Min. :0.000 Min. : 0.000
## 1st Qu.:-2.084 1st Qu.: 40.56 1st Qu.:1.121 1st Qu.: 6.725
## Median :-1.492 Median : 68.07 Median :2.226 Median : 8.456
## Mean :-1.511 Mean : 78.78 Mean :2.728 Mean : 8.706
## 3rd Qu.:-1.059 3rd Qu.:111.92 3rd Qu.:4.343 3rd Qu.:10.601
## Max. : 0.693 Max. :213.22 Max. :5.837 Max. :14.627
##
## pf pfChart desc pf.range
## Min. :0.8934 Min. :0.9986 Lagging: 5 (0.98,1] :123
## 1st Qu.:0.9616 1st Qu.:1.0052 Leading:235 (0.96,0.98]: 59
## Median :0.9814 Median :1.0186 (0.92,0.94]: 22
## Mean :0.9723 Mean :1.0277 (0.94,0.96]: 19
## 3rd Qu.:0.9948 3rd Qu.:1.0384 (0.90,0.92]: 13
## Max. :1.0000 Max. :1.1066 (Other) : 3
## NA's :1 NA's :1 NA's : 1
This chart demonstrates how the voltage can vary on the lower and upper ends of the voltage ranges.
investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?
The voltage and power factor for the entire system seem to track or follow a similar trend here. They have similar shapes. Or at least when the power factor range increases the voltage drops less in the system. This could be for many reasons.
One idea to be explored is if we can predict when the power factor will go below 0.98 lagging or leading. This could help us change the system parameters to keep the network in operating efficiency. ## Goals * Create model for each substation to predict when power factor goes below 0.98 based on the hourly readings. If we can predict at a minimum 2 hours ahead this would be idea. The initial
##
## Calls:
## m1: lm(formula = pf ~ I(sqrt(mw)), data = powerfactor_tidy)
## m2: lm(formula = pf ~ I(sqrt(mw)) + mw, data = powerfactor_tidy)
## m3: lm(formula = pf ~ I(sqrt(mw)) + mvar, data = powerfactor_tidy)
## m4: lm(formula = pf ~ I(sqrt(mw)) + mw + h, data = powerfactor_tidy)
## m5: lm(formula = pf ~ I(sqrt(mw)) + mvar + desc, data = powerfactor_tidy)
##
## ================================================================================
## m1 m2 m3 m4 m5
## --------------------------------------------------------------------------------
## (Intercept) 0.955*** 0.864*** 0.967*** 0.871*** 0.970***
## (0.002) (0.005) (0.002) (0.005) (0.002)
## I(sqrt(mw)) 0.009*** 0.072*** 0.005*** 0.071*** 0.006***
## (0.001) (0.004) (0.001) (0.004) (0.001)
## mw -0.010*** -0.010***
## (0.001) (0.001)
## mvar 0.003*** 0.001
## (0.000) (0.000)
## h -0.000***
## (0.000)
## desc: Leading/Lagging -0.008***
## (0.001)
## --------------------------------------------------------------------------------
## R-squared 0.1 0.2 0.1 0.2 0.1
## adj. R-squared 0.1 0.1 0.1 0.2 0.1
## sigma 0.0 0.0 0.0 0.0 0.0
## F 254.5 295.1 184.0 235.5 139.9
## p 0.0 0.0 0.0 0.0 0.0
## Log-likelihood 8257.4 8406.7 8309.4 8455.5 8332.7
## Deviance 1.4 1.3 1.4 1.2 1.3
## AIC -16508.8 -16805.3 -16610.8 -16901.0 -16655.3
## BIC -16490.5 -16780.9 -16586.3 -16870.4 -16624.7
## N 3345 3345 3345 3345 3345
## ================================================================================
Expected Result : 0.9903636
## fit lwr upr
## 1 0.9935461 0.9542009 1.032891
##
## Call:
## lm(formula = pf ~ I(sqrt(mw)) + mvar + desc, data = powerfactor_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.110210 -0.007643 0.006219 0.013327 0.029249
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9700961 0.0020414 475.208 < 2e-16 ***
## I(sqrt(mw)) 0.0055247 0.0006944 7.956 2.40e-15 ***
## mvar 0.0005560 0.0003866 1.438 0.15
## descLeading -0.0083754 0.0012239 -6.843 9.18e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02005 on 3341 degrees of freedom
## (255 observations deleted due to missingness)
## Multiple R-squared: 0.1116, Adjusted R-squared: 0.1108
## F-statistic: 139.9 on 3 and 3341 DF, p-value: < 2.2e-16
## Analysis of Variance Table
##
## Response: pf
## Df Sum Sq Mean Sq F value Pr(>F)
## I(sqrt(mw)) 1 0.10698 0.106981 266.065 < 2.2e-16 ***
## mvar 1 0.04300 0.042998 106.937 < 2.2e-16 ***
## desc 1 0.01883 0.018829 46.829 9.178e-12 ***
## Residuals 3341 1.34338 0.000402
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Are the final three plots varied and do they meet some of the following criteria:
1 Draw comparisons.
2 Identify trends.
3 Engage a wide audience.
4 Explain a complicated finding.
5 Clarify a gap between perception and reality.
6 Enable the reader to digest large amounts of information.
Each plot reveals an important and different comparison or trend in the data. The plots incorporate many of the variables from the data set in a way that allows the plots to convey a lot of information while still being interpreted easily. The plots fulfill 4 or more of the criteria.
Voltage and Power Factor Outlier plot helps the user to quickly identify which substations are out the bounded region.
This chart represents the voltage and power factor for all data points collected for 2016-03-02. The chart allows one to see how much of the data falls out of the voltage and power factor defined region (0.98 (left) to 0.99 (right), and 114v to 126v).
We can see we have more points with Lagging power factors outside the required range for efficient power factor values.
NEED 4 or more…
1 Draw comparisons. * YES - Comparisons between substations 2 Identify trends.
* NO - Trends - Nope, need multiple days… or day without VVar day with VVar 3 Engage a wide audience. * Yes, easy to review… 4 Explain a complicated finding.
* YES - which substations behaved and what where their min and max for pf and voltages 5 Clarify a gap between perception and reality.
* MAYBE - If a person looks at the current momentary… status * the daily status might be different 6 Enable the reader to digest large amounts of information. * YES - Power Factor, Voltage, Ranges, inside the comfort zone,
Heatmap of Voltage to help user to see how all substations performed during each 15 minute period during the day. One chart helps to see who is in the red (low) or in the purple (high) voltage ranges.
1 Draw comparisons.
2 Identify trends.
3 Engage a wide audience.
4 Explain a complicated finding.
5 Clarify a gap between perception and reality.
6 Enable the reader to digest large amounts of information.
Description goes here please… Note, I think I have a better plot to put here, this one kinda goes along with Plot_One, it is just another form of the plot.
Total
I was interested in finding substations where the voltage has high varience and to see what affect this has on the power factor. When reviewing this data day to day variations are affected by the voltage requlators to help reduce the voltage on the transmission lines. A voltage load profile with less varience should have a better power factor (what does better mean, 0.98-1, lagging or leading?[2]
Identify which days have VVC (Volt Var Contol On). 3/2 off 3/3 On — Walter Has these notes.
The section explains any important decisions in the analysis and how those decisions affected the analysis.
Need to make sure to handle cases when data is missing from a day over a few date ranges.
Automate additional processes.
Voltage seems to be normally like distributed by the hour through out the day and by substation for the entire by hour. This seems good since large flucuations in voltage are bad for consumers and commercial businesses.
Power Factor can flucuation from lagging to leading in on substation in a single day. This requires more effort to control the voltage , watts, and vars across the power lines. Can I show that when voltage is tightly controled we have less variability in the power factor??????
TODO: Find a sub with the best range in voltage and look at its power factor. Then compare it’s MW and MVARS to all other substations.
The section reflects on how the analysis was conducted and reports on the struggles and successes throughout the analysis. The section provides at least one idea or question for future work.
The section provides a rich and well-written reflection of * struggles * Date Formatting without lubridate was one mistake or line of code which would not run. * Exploring for relationships - In industry standards it is typically regarded as controling voltage with less varience helps keep the power factor with in nominal ranges. When looking for the correlation between power factor and votlage we really can not see one most likely because the voltage is in a narrow range, and power factor is more affected by kw and mvars since it is a ratio of real / active power.
The section poses ideas or questions for future work. * multiple days would be benficial * months to months * 12 month analysis of trends * seasonal trends * collect more power factor data down to 15min intervals * examining the varience of all the load shapes for each variable. * revewing the load shape for all meters on every substation.
We monitor voltage since a utility can change the voltage across the power lines. Keeping the system balanced at low voltages between 114 and 126 helps to improve the efficeny of the power transmission since lower voltages mean less resistance.
I = Current
R = Resistance
V = Voltage
\(V = I*R\)
\(R = \frac{V}{I}\)
\(I = \frac{V}{R}\)
P(kW) = PF × I(A) × V(V) / 1000
Power - kW, kiloWatts
Power Factor
I - Amps
Voltage - Volts
3 Phase
P(kW) = √3 × PF × I(A) × VL-L(V) / 1000
P, Real Power - kW -> PMWD3D (MW) Real power is kilowatts, in the initial dataset this is represented as PMWD3D.
S, Apparent Power (volt amperess) We will be solving for apparent power.
Q, Reactive Power Reactive power is kVAR, in the initial dataset PMQD3D is Delivered and
PMQR3D is Received. The total kVars are (PMQD3D-PMQR3D).
\(S^2 = P^2 + Q^2\)
\(S=\sqrt{P^2 + Q^2}\)
The power factor is defined as the ratio of real power to apparent power.
\[Power Factor=\frac{P}{\sqrt{P^2 + Q^2}}\]
\[Power Factor =\frac{kW}{\sqrt{kW^2 + (kVAR Delieverd - kVAR Received)^2}}\]
[1] https://en.wikipedia.org/wiki/Power_factor [2] https://en.wikipedia.org/wiki/Distribution_management_system#Volt-VAR_Control_.28VVC.29 https://en.wikipedia.org/wiki/Ohm%27s_law
https://en.wikipedia.org/wiki/Volt-ampere_reactive
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